Solve g(t)dt=g(-t)(-dt)

$$g ( t ) d t = g ( - t ) ( - d t )$$

Solve for d (complex solution)

$$d\in \mathrm{C}$$

Solution Steps

Multiply t and t to get t^{2}.

$$gt^{2}d=g\left(-t\right)\left(-d\right)t$$

Subtract g\left(-t\right)\left(-d\right)t from both sides.

$$gt^{2}d-g\left(-t\right)\left(-d\right)t=0$$

Multiply t and t to get t^{2}.

$$gt^{2}d-g\left(-1\right)t^{2}\left(-1\right)d=0$$

Multiply -1 and -1 to get 1.

$$gt^{2}d+gt^{2}\left(-1\right)d=0$$

Combine gt^{2}d and gt^{2}\left(-1\right)d to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any d.

$$d\in \mathrm{C}$$

Solve for g (complex solution)

$$g\in \mathrm{C}$$

Solution Steps

Multiply t and t to get t^{2}.

$$gt^{2}d=g\left(-t\right)\left(-d\right)t$$

Subtract g\left(-t\right)\left(-d\right)t from both sides.

$$gt^{2}d-g\left(-t\right)\left(-d\right)t=0$$

Multiply t and t to get t^{2}.

$$gt^{2}d-g\left(-1\right)t^{2}\left(-1\right)d=0$$

Multiply -1 and -1 to get 1.

$$gt^{2}d+gt^{2}\left(-1\right)d=0$$

Combine gt^{2}d and gt^{2}\left(-1\right)d to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any g.

$$g\in \mathrm{C}$$

Solve for d

$$d\in \mathrm{R}$$

Solution Steps

Multiply t and t to get t^{2}.

$$gt^{2}d=g\left(-t\right)\left(-d\right)t$$

Subtract g\left(-t\right)\left(-d\right)t from both sides.

$$gt^{2}d-g\left(-t\right)\left(-d\right)t=0$$

Multiply t and t to get t^{2}.

$$gt^{2}d-g\left(-1\right)t^{2}\left(-1\right)d=0$$

Multiply -1 and -1 to get 1.

$$gt^{2}d+gt^{2}\left(-1\right)d=0$$

Combine gt^{2}d and gt^{2}\left(-1\right)d to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any d.

$$d\in \mathrm{R}$$

Solve for g

$$g\in \mathrm{R}$$

Solution Steps

Multiply t and t to get t^{2}.

$$gt^{2}d=g\left(-t\right)\left(-d\right)t$$

Subtract g\left(-t\right)\left(-d\right)t from both sides.

$$gt^{2}d-g\left(-t\right)\left(-d\right)t=0$$

Multiply t and t to get t^{2}.

$$gt^{2}d-g\left(-1\right)t^{2}\left(-1\right)d=0$$

Multiply -1 and -1 to get 1.

$$gt^{2}d+gt^{2}\left(-1\right)d=0$$

Combine gt^{2}d and gt^{2}\left(-1\right)d to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any g.

$$g\in \mathrm{R}$$